Question

The standard entropy change for the reaction: \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SO}_{3}(\mathrm{~g})\) is (where \(\mathrm{S}^{\circ}\) for \(\mathrm{SO}_{2}\) (g), \(\mathrm{O}_{2}(\mathrm{~g})\) and \(\mathrm{SO}_{3}(\mathrm{~g})\) are \(248.5,205\) and \(256.2\) J \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) respectively) (a) \(198.2 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \quad\) (b) \(-192.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) (c) \(-94.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) (d) \(94.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)

Short answer

The standard entropy change for the reaction is \(-94.8 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1}\) (option c).

Step-by-step solution

Understand the Standard Entropy Change

The standard entropy change of a reaction, \( \Delta S^{\circ} \), is calculated using the standard entropies of the reactants and products. The formula used is \( \Delta S^{\circ} = S^{\circ}_{\text{products}} - S^{\circ}_{\text{reactants}} \). This means we need to find the difference between the sum of the entropies of the products and the reactants.

List the Given Entropies

We have the standard entropies for \( \mathrm{SO}_2(g) \), \( \mathrm{O}_2(g) \), and \( \mathrm{SO}_3(g) \):- \( S^{\circ}_{\mathrm{SO}_2} = 248.5 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \)- \( S^{\circ}_{\mathrm{O}_2} = 205 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \)- \( S^{\circ}_{\mathrm{SO}_3} = 256.2 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \)

Key concepts

Standard Entropy Change

In thermodynamics, the standard entropy change, represented as \( \Delta S^{\circ} \), is a useful measurement in evaluating the randomness or disorder within a chemical reaction. It allows us to understand the energy distribution at the molecular level. The symbol \( S^{\circ} \) stands for the standard entropy of a substance, which represents the entropy at a specific pressure (usually 1 bar) and a given temperature (usually 298 K). Calculating \( \Delta S^{\circ} \) involves subtracting the sum of the standard entropies of the reactants from the sum of the standard entropies of the products. This can be expressed through the formula:

• \( \Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}} \)

This formula helps chemists predict whether a reaction will lead to an increase or decrease in disorder. A positive \( \Delta S^{\circ} \) indicates greater disorder, while a negative value suggests reduced disorder. For instance, in the given exercise where sulfur dioxide reacts with oxygen to form sulfur trioxide, understanding the entropy change can give insights into whether the reaction becomes more or less random.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into different substances, known as products. They are accompanied by energetic changes, including changes in enthalpy (heat) and entropy (disorder).In the context of thermodynamics, the focus is often on analyzing how these energetic changes affect the spontaneity and feasibility of the reaction. The reaction between sulfur dioxide (\( \mathrm{SO}_2 \)) and oxygen (\( \mathrm{O}_2 \)) to form sulfur trioxide (\( \mathrm{SO}_3 \)) is a typical example of a chemical reaction studied in thermodynamics.
For every chemical reaction, it’s crucial to balance the equation to adhere to the law of conservation of mass. This balancing extends to calculating the number of moles of reactants and products, which is essential for understanding and applying the entropy and enthalpy concepts precisely.
As we calculate properties like standard entropy change, balancing the chemical equation helps ensure that the ratios of entropies correctly reflect the scale of the reaction. It is this meticulous balancing that allows chemists to make accurate predictions about the behavior of the reactions under standard conditions.

• Reactants: \( \mathrm{SO}_2(g) \), \( \mathrm{O}_2(g) \)
• Product: \( \mathrm{SO}_3(g) \)

Entropy Calculation

Entropy calculations are critical for understanding how a chemical reaction progresses in terms of disorder. The calculation of entropy changes during a reaction involves basic arithmetic based on the entropies provided for the standardized conditions. Let’s break down the process:

• Identify the standard entropies for all substances involved: \( S^{\circ}_{\mathrm{SO}_2} = 248.5 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \), \( S^{\circ}_{\mathrm{O}_2} = 205 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \), \( S^{\circ}_{\mathrm{SO}_3} = 256.2 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \).
• Apply the entropy formula: \( \Delta S^{\circ} = S^{\circ}_{\mathrm{SO}_3} - (S^{\circ}_{\mathrm{SO}_2} + \frac{1}{2}S^{\circ}_{\mathrm{O}_2}) \).

Substitute the values into the formula:

• \( \Delta S^{\circ} = 256.2 - (248.5 + 0.5 \times 205) = 256.2 - 351 \)
• This results in \( \Delta S^{\circ} = -94.8 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{mol}^{-1} \).

The negative value signifies that the reaction results in a decrease in disorder, often associated with gas molecule conversion to fewer moles, as observed in the reaction from gases \( \mathrm{SO}_2 \) and \( \mathrm{O}_2 \) to a single product gas \( \mathrm{SO}_3 \). Understanding this helps predict reaction spontaneity and extent.